Abstract:

Probabilistic generative models are robust to noise, uncover unseen patterns, and make predictions
about the future. These models have been used successfully to solve problems in
neuroscience, astrophysics, genetics, and medicine. The main computational challenge is
computing the hidden structure given the data—posterior inference. For most models of
interest, computing the posterior distribution requires approximations like variational inference.
Variational inference transforms posterior inference into optimization. Classically,
this optimization problem was feasible to deploy in only a small fraction of models.
This thesis develops black box variational inference. Black box variational inference is
a variational inference algorithm that is easy to deploy on a broad class of models and has
already found use in models for neuroscience and health care. It makes new kinds of models
possible, ones that were too unruly for previous inference methods.
One set of models we develop is deep exponential families. Deep exponential families
uncover new kinds of hidden pattens while being predictive of future data. Many existing
models are deep exponential families. Black box variational inference makes it possible for
us to quickly study a broad range of deep exponential families with minimal added effort
for each new type of deep exponential family.
The ideas around black box variational inference also facilitate new kinds of variational
methods. First, we develop hierarchical variational models. Hierarchical variational models
improve the approximation quality of variational inference by building higher-fidelity
approximations from coarser ones. We show that they help with inference in deep exponential
families. Second, we introduce operator variational inference. Operator variational
inference delves into the possible distance measures that can be used for the variational optimization
problem. We show that this formulation categorizes various variational inference
methods and enables variational approximations without tractable densities.
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By developing black box variational inference, we have opened doors to new models, better
posterior approximations, and new varieties of variational inference algorithms.